We develop parameter-robust numerical algorithms for Biot modeland apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction-diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms
are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by the abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters onbrain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; Young’s modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influences on the tissue deformation and the developing speed of brain swelling.
Dr. Cai is an associate professor of Mathematics from Morgan State University. His research is in the field of numerical analysis with focuses on numerical methods for partial differential equations, computational biomechanics, and fast algorithms for data science. His main interest is to develop fast solvers for partial differential equations and their applications in biomechanics, material science, environmental science and geoscience.
Dr. Cai graduated from Hong Kong University of Science and Technology in 2008 and joined Morgan State University in 2015. He has around 30 publication and received several major grants from NSF and NIH.